Randomized gap and amplitude estimation

Abstract

Methods and apparatus are provided that permit estimation of eigenphase or eigenvalue gaps in which random or pseudo-random unitaries are applied to a selected initial quantum state to produce a random quantum state. A target unitary is then applied to the random quantum state one or more times, or an evolution time is allowed to elapse after application of the target unitary. An inverse of the pseudo-random unitary used to produce the random quantum state is applied, and the resultant state is measured with respect to the initial quantum state. Measured values are used to produce Bayesian updates, and eigenvalue / eigenvector gaps are estimated. In some examples, the disclosed methods are used in amplitude estimate and control map determinations. Eigenvalue gaps for time-dependent Hamiltonians can be evaluated by adiabatic evolution of the Hamiltonian from an initial Hamiltonian to a final Hamiltonian.

Description

FIELD OF THE INVENTION[0001]The invention pertains to eigenphase determination in quantum computing.BACKGROUND OF THE INVENTION[0002]Phase estimation is a technique of fundamental importance to quantum computing. It is not only necessary for the exponential speedup in Shor's factoring algorithm but also is responsible for quadratic performance improvements in quantum simulation. The goal of phase estimation is to estimate the eigenvalue associated with an input eigenstate, or more generally to sample from the eigenvalues in the support of an input state vector. This process works by using a control register that is prepared in a quantum superposition and then a unitary, whose eigenvalues are sought, is applied to the system controlled a number of times that is specified by the value of the control register. There are several ways that this process can be performed but a commonality between them is that all of these approaches require at least one qubit to control the process as well...

AI Technical Summary

Benefits of technology

The patent is about a method for estimating the value of a quantum operator's eigenvector or eigenphase. This is done by applying a random or pseudo-random unitary to an initial quantum state and then measuring the resulting quantum state with respect to the initial state. The measurement results are used to update a Bayesian estimate. The method can be used in quantum computation systems and has applications in determining control maps and eigenvalue gaps in time-dependent Hamiltonians.

Problems solved by technology

The need for external control substantially limits the uses of phase estimation on existing hardware not only because of the additional cost of ancilla qubits, but also because controlled operations are typically much more difficult to perform than corresponding uncontrolled operations.

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